A372913 Decimal expansion of (1/31)*(14*sqrt(5 - 2*sqrt(5)) + 4*sqrt(5 + 2*sqrt(5))).

7, 2, 5, 2, 3, 6, 4, 3, 6, 7, 9, 9, 2, 2, 7, 9, 3, 5, 8, 9, 7, 3, 4, 5, 0, 6, 1, 5, 7, 6, 6, 5, 4, 8, 9, 6, 4, 7, 2, 6, 4, 8, 4, 5, 4, 0, 5, 3, 6, 8, 0, 2, 6, 4, 0, 8, 5, 7, 2, 7, 5, 3, 4, 9, 7, 8, 7, 0, 7, 8, 9, 1, 6, 0, 7, 0, 9, 4, 4, 1, 6, 5, 0, 6, 6, 6

Offset

0,1

Links

Table of n, a(n) for n=0..85.

Index entries for algebraic numbers, degree 4.

Formula

Equals Sum_{k>=0} tan(k*Pi/5)/2^k.

Minimal polynomial 923521*x^4 -2037320*x^2 +816080 . - R. J. Mathar, Jun 03 2026

Example

0.72523643679922793589734506157665489647264845405...

Maple

sqrt(265-62*sqrt(5)) ; %*2/31 ; evalf(%) ; # R. J. Mathar, Aug 02 2024

Mathematica

s = Sum[Tan[k Pi/5]/2^k, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]
N[1/31 (14 Sqrt[5 - 2 Sqrt[5]] + 4 Sqrt[5 + 2 Sqrt[5]]), 100]

Prog

(PARI) (14*sqrt(5-2*sqrt(5))+4*sqrt(5+2*sqrt(5)))/31 \\ Charles R Greathouse IV, May 13 2026
(PARI) polrootsreal(923521*x^4-2037320*x^2+816080)[3] \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A372912, A372914.

Sequence in context: A344761 A344762 A093072 * A366599 A352890 A066903

Adjacent sequences: A372910 A372911 A372912 * A372914 A372915 A372916

Keyword

nonn,cons

Author

Clark Kimberling, Jul 01 2024

Status

approved